A rubber ball dropped on a hard surface takes a sequence of bounces, each one 4/5 as high as the preceding one. If this ball is dropped from a height of 10 feet, what is the total vertical distance it has traveled at the time when it hits the surface for its fifth bounce?

Answer 1

To find the total vertical distance the ball has traveled at the time of its fifth bounce, we can sum up the distances it travels during each bounce.

When dropped from a height of 10 feet, the ball bounces to a height of 10 * 4/5 = 8 feet after the first bounce.

After the second bounce, the ball reaches a height of 8 * 4/5 = 6.4 feet.

After the third bounce, the ball reaches a height of 6.4 * 4/5 = 5.12 feet.

After the fourth bounce, the ball reaches a height of 5.12 * 4/5 = 4.096 feet.

After the fifth bounce, the ball reaches a height of 4.096 * 4/5 = 3.2768 feet.

So, the total vertical distance the rubber ball has traveled at the time of its fifth bounce is 10 + 8 + 6.4 + 5.12 + 4.096 + 3.2768 = 36.8768 feet.